Finite Group Databasebeta

← #11897559

Subgroups — #11897559

Order 1152.

802 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×Dic6C211yesmaximal, characteristic, complemented
2#10593960C211yesmaximal, characteristic, complemented
3#10592707C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic
5#10591430C212yesmaximal
6#10591409C212yesmaximal, complemented
7#10590465C212yesmaximal, complemented
8#10590420C212yesmaximal, complemented
9#10590303C211yesmaximal, characteristic, complemented
10#10590269C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83564—31nomaximal
13#79576—31nomaximal
14C22×C3×Dic6—21no—
15C32×C4×D4C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×D4×Dic3C2212yes—
18C2×C3×#213C2211yescharacteristic
19C3×#924—21no—
20C3×#888C2212yes—
21C3×#878—22no—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12C2212yes—
27D3×C4⋊Dic3—21no—
28#63869C2212yes—
29#63856—21no—
30#63659C2212yes—
31#63635C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#807C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63576C2212yes—
38#63573C2212yes—
39#63573C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×D4×Q8—31no—
44#5579—31no—
45#5543—31no—
46D4×Dic6D311yescharacteristic, complemented
47C3×C4×D8—31no—
48#5152—32no—
49#5087—31no—
50#5084—32no—
51#5081—32no—
52#5080—31no—
53#5024—31no—
54#5014—32no—
55C4×#213D311yescharacteristic
56#5009—32no—
57#5008—31no—
58#5008—31no—
59#5008—61no—
60#5007—31no—
61#4876—32no—
62#4763—32no—
63#4761—32no—
64#4680—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634—21no—
69C22×C3×Dic3—22no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6—44no—
75C2×C3×Dic6D411yescharacteristic
76C2×D3×Dic3—22no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×#217—22no—
84C3×#213Q814yescomplemented
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3724—22no—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3384—91noSylow
99C22×C3×Q8—61no—
100C22×Dic6—21no—
101C2×C3×D8—31no—
102C3×C4⋊Q8—32no—
103C3×C4⋊Q8—31no—
104C3×C22⋊Q8—62no—
105C3×C22⋊Q8—61no—
106C3×C4×Q8—31no—
107C3×C4×D4—21no—
108C3×C4×D4—32no—
109C3×C4×D4—31no—
110C3×C4×D4C2×D311yescharacteristic
111C3×C4×D4C2×D311yescharacteristic
112#946—61no—
113D4×Dic3—32no—
114D4×Dic3C2×D312yes—
115C2×#213C2×D311yescharacteristic
116C2×C4⋊Dic3—61no—
117#924—21no—
118#924—61no—
119#896—62no—
120D3×C4⋊C4—61no—
121#890—32no—
122#888C2×D312yes—
123#878—22no—
124#878—62no—
125C4×D12—32no—
126C4×D12C2×D311yescharacteristic
127#870—32no—
128#869—31no—
129#869—31no—
130#869—61no—
131#869C2×D311yescharacteristic
132C4×Dic6C2×D311yescharacteristic
133C3×#107—31no—
134C3×#102—31no—
135C3×#102—31no—
136C3×C4×C8—31no—
137#832—32no—
138#832—32no—
139#832—32no—
140#832—62no—
141#832C2×D311yescharacteristic
142#817—32no—
143#817—32no—
144#815—32no—
145Dic3⋊C8—32no—
146#809—32no—
147#809C2×D311yescharacteristic
148#808—32no—
149#808—32no—
150#808—32no—
151#808—32no—
152#808—62no—
153#807—32no—
154#807—32no—
155#807C2×D311yescharacteristic
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160#803—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C23×C32—21no—
163C22×C3×D3—21no—
164C32×D4—21no—
165C32×D4C2×Q812yes—
166C2×C32×C4—21no—
167C2×C32×C4—42no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172#634—81no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—44no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—21no—
179C3×D12C2×Q812yescomplemented
180C3×C4×D3—42no—
181C3×Dic6—22no—
182C3×Dic6—44no—
183C3×Dic6—42no—
184D3×Dic3—82no—
185C3⋊(C3⋊C8)—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8C2×Q812yescomplemented
188#554—91no—
189D4×Q8—31no—
190#501—92no—
191#498—91no—
192#478—92no—
193#476—92no—
194#476—91no—
195#474—91no—
196#446—91no—
197#442—92no—
198C4×D8—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8—62no—
201C2×C3×Q8—61no—
202C2×C3×Q8—124no—
203C2×C3×D4—21no—
204C2×C3×D4—31no—
205C2×C3×D4C22×D311yescharacteristic
206C2×C3×D4C22×D311yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—41no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212C22×Dic3—22no—
213C22×Dic3—62no—
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—62no—
217C2×Dic6—21no—
218C2×Dic6—22no—
219C2×Dic6—44no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—121no—
223C2×Dic6#6711yescharacteristic
224C3×D8—34no—
225C2×C3×C8—31no—
226C2×C3×C8—31no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—41no—
239C3×C22⋊C4—62no—
240C3×C22⋊C4—61no—
241C3×C42—21no—
242C3×C42—32no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#217—22no—
246#217—62no—
247#213Dic614yescomplemented
248(C2×D3)⋊C4—21no—
249(C2×D3)⋊C4—62no—
250C4⋊Dic3—21no—
251C4⋊Dic3—32no—
252C4⋊Dic3—32no—
253C4⋊Dic3—62no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—62no—
257C4⋊Dic3—121no—
258C4⋊Dic3#6711yescharacteristic
259C4⋊Dic3C22×D311yescharacteristic
260C4⋊Dic3C22×D312yes—
261Dic3⋊C4—22no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4#6712yes—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8C22×D311yescharacteristic
271C2×C3⋊C8C22×D311yescharacteristic
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C32×C4—21no—
280C32×C4—41no—
281C32×C4AGL(1,ℤ/8)12yes—
282C32×C4C22×Q811yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—42no—
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C22×Q8—61no—
290C2×D8—31no—
291C4⋊Q8—32no—
292C4⋊Q8—31no—
293C4⋊Q8—91no—
294#125—92no—
295C22⋊Q8—62no—
296C22⋊Q8—61no—
297C22⋊Q8—182no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×D4—32no—
301C4×D4—31no—
302C4×D4—92no—
303C4×D4D3211yescharacteristic
304C2×C4⋊C4—181no—
305#107—31no—
306#107—92no—
307#106—92no—
308#106—92no—
309#106—92no—
310C4⋊C8—92no—
311C4⋊C8—91no—
312#102—31no—
313#102—31no—
314#102—92no—
315#102—92no—
316#97—92no—
317C4×C8—31no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—41no—
321C23×C3—61no—
322C22×D3—21no—
323C3×Q8—62no—
324C3×Q8—124no—
325C3×Q8—122no—
326C3×D4—21no—
327C3×D4—21no—
328C3×D4—22no—
329C3×D4—32no—
330C3×D4—41no—
331C3×D4—61no—
332C3×D4C2×Dic612yes—
333C3×D4D3×Q812yes—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—41no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—62no—
345C2×C3×C4—61no—
346C2×C3×C4—82no—
347C2×C3×C4—124no—
348C2×C3×C4—122no—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—44no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—242no—
362C2×Dic3C2×#6712yes—
363C2×Dic3C2×#6712yes—
364D12—21no—
365D12C2×Dic612yescomplemented
366C4×D3—42no—
367C4×D3—242no—
368Dic6—22no—
369Dic6—44no—
370Dic6—42no—
371Dic6—241no—
372Dic6—241no—
373Dic6—242no—
374C3×C8—32no—
375C3×C8—61no—
376C3⋊C8—21no—
377C3⋊C8—62no—
378C3⋊C8—62no—
379C3⋊C8—122no—
380C3⋊C8C2×Dic612yescomplemented
381C2×C32—42no—
382C2×C32D4×Q811yescharacteristic
383C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
384C2×C32#57711yescharacteristic
385C3×D3—42no—
386C2×Q8—31no—
387C2×Q8—62no—
388C2×Q8—61no—
389C2×Q8—124no—
390C2×Q8—181no—
391C2×D4—31no—
392C2×D4C2×D3211yescharacteristic
393C22×C4—21no—
394C22×C4—62no—
395C22×C4—61no—
396C22×C4—182no—
397D8—34no—
398C2×C8—31no—
399C2×C8—31no—
400C2×C8—92no—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—31no—
404C4⋊C4—32no—
405C4⋊C4—62no—
406C4⋊C4—61no—
407C4⋊C4—92no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C4⋊C4C2×D3211yescharacteristic
412C22⋊C4—21no—
413C22⋊C4—62no—
414C22⋊C4—61no—
415C22⋊C4—182no—
416C42—32no—
417C42C2×D3211yescharacteristic
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—42no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—62no—
427C22×C3—81no—
428C22×C3—81no—
429C22×C3—121no—
430C22×C3—121no—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C22×#6711yescharacteristic
433C2×D3—22no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—62no—
445C3×C4—62no—
446C3×C4—81no—
447C3×C4—122no—
448C3×C4—121no—
449C3×C4#91112yes—
450C3×C4#93212yes—
451C3×C4C22×Dic611yescharacteristic
452C3×C4C2×D3×Q811yescharacteristic
453C3×C4#100711yescharacteristic
454C3×C4#101011yescharacteristic
455Dic3—22no—
456Dic3—22no—
457Dic3—41no—
458Dic3—42no—
459Dic3—122no—
460Dic3—122no—
461Dic3—242no—
462C32#338411yescharacteristic, complemented, Sylow
463C23—21no—
464C23—61no—
465Q8—62no—
466Q8—124no—
467Q8—122no—
468Q8—721no—
469D4—21no—
470D4—32no—
471D4—61no—
472D4D3×Dic612yes—
473C2×C4—21no—
474C2×C4—32no—
475C2×C4—32no—
476C2×C4—42no—
477C2×C4—62no—
478C2×C4—61no—
479C2×C4—124no—
480C2×C4—122no—
481C2×C4—182no—
482C2×C4—722no—
483C2×C4D3×#6711yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—32no—
487C8—61no—
488C8—182no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—42no—
493C2×C3—42no—
494C2×C3—82no—
495C2×C3—122no—
496C2×C3D4×Dic611yescharacteristic
497C2×C3C2×#91111yescharacteristic
498C2×C3#577011yescharacteristic
499C2×C3C2×#93211yescharacteristic
500C2×C3Q8×#6711yescharacteristic
501C2×C3#583711yescharacteristic
502D3—42no—
503C22—22no—
504C22—41no—
505C22—41no—
506C22—62no—
507C22—121no—
508C22—121no—
509C22C2×D3×#6711yescharacteristic
510C4—21no—
511C4—41no—
512C4—62no—
513C4—62no—
514C4—122no—
515C4—121no—
516C4—362no—
517C4#6393212yes—
518C4C2×D3×Dic611yescharacteristic
519C4#6429711yescharacteristic
520C3—21no—
521C3#7957611yescharacteristic, complemented
522C3#8356411yescharacteristic, complemented
523C2—42no—
524C2—122no—
525C2Dic6×#6711yescharacteristic
526C2C2×#6393211yescharacteristic
527C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×D4×Dic6C2semidirect
2. #10593960C2semidirect
3. #10592707C2semidirect
6. #10591409C2semidirect
7. #10590465C2semidirect
8. #10590420C2semidirect
9. #10590303C2semidirect
10. #10590269C2semidirect
11. #10590258C2semidirect
46. D4×Dic6D3semidirect
84. C3×#213Q8semidirect
179. C3×D12C2×Q8semidirect
187. C3×C3⋊C8C2×Q8semidirect
247. #213Dic6semidirect
365. D12C2×Dic6semidirect
380. C3⋊C8C2×Dic6semidirect
462. C32#3384semidirect
521. C3#79576semidirect
522. C3#83564semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×D4×Dic62
#105939602
#105927072
C3×C4×#2132
#105914302
#105914092
#105904652
#105904202
#105903032
#105902692
#105902582
#835643
#795763